SOLUTION: Please, someone help me with that. Verify algebrically if the equation is an identity. Cos(x)/Sec(x)*Sin(x)= Csc(x)- Sin(x)

Algebra ->  Trigonometry-basics -> SOLUTION: Please, someone help me with that. Verify algebrically if the equation is an identity. Cos(x)/Sec(x)*Sin(x)= Csc(x)- Sin(x)      Log On


   

Question 969333: Please, someone help me with that. Verify algebrically if the equation is an identity.
Cos(x)/Sec(x)*Sin(x)= Csc(x)- Sin(x)
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Equivalent to given: Cos%28x%29%2FSec%28x%29%2ASin%28x%29=+Csc%28x%29-+Sin%28x%29

Left side:
%28cos%28x%29sin%28x%29%29%2F%281%2Fcos%28x%29%29

cos%28x%29sin%28x%29cos%28x%29

cos%5E2%28x%29sin%28x%29

%281-sin%5E2%28x%29%29sin%28x%29
This is a difficult path of steps, so starting new with ....


The right-hand side:
csc%28x%29-sin%28x%29

1%2Fsin%28x%29-sin%28x%29

1%2Fsin%28x%29-sin%5E2%28x%29%2Fsin%28x%29

%281-sin%5E2%28x%29%29%2Fsin%28x%29

cos%5E2%28x%29%2Fsin%28x%29

cos%28x%29%28cos%28x%29%2Fsin%28x%29%29---------Almost resembles the left side, but not fully yet. We must be able to show that cos%28x%29%2Fsin%28x%29 is identical to sin%28x%29%2Fsec%28x%29. Is this a truth?
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Trying to work with those two smaller or simpler expressions;
sin%28x%29%2Fsec%28x%29
sin%28x%29%2F%281%2Fcos%28x%29%29
sin%28x%29cos%28x%29, NO! Not the same!
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cos%28x%29%2Fsin%28x%29%3C%3Esin%28x%29%2Fsec%28x%29

Your original equation is NOT an identity.